JP3605649B2 - Surface profile measuring method and device - Google Patents

Description

【０００７】
ここで、ａ＝−Ｌｂ／（Ｌａ＋Ｌｂ）、ｂ＝−Ｌａ／（Ｌａ＋Ｌｂ）及びΔｋ＝ｋＢ＋ａ・ｋＡ＋ｂ・ｋＣとおいて、ａを（１）式にかけ、ｂを（３）式にかけて、（１）、（２）、（３）式を加えて並進誤差Ｅｚ（Ｘ）及びピッチング誤差Ｅｐ（Ｘ）を消去することにより、次の（４）式に示すような合成測定量Ｙ（Ｘ）が得られる。
【０００８】

【０００９】
又、被測定物１２の測定対象長さをＬとして、表面プロフィール形状ｍ（Ｘ）が次の（５）式に示すようなフーリエ級数の和の形で表わされるとする。
【００１０】
【数１】

【００１１】
この（５）式を（４）式に代入して整理すると、次の（６）〜（９）式が得られる。
【００１２】
【数２】

【００１３】

【００１４】
（７）、（８）式のｆｊ及びδｊは被測定物表面プロフィールｍ（Ｘ）によらない定数であるから、測定値から求まるデータ列Ｙ（Ｘ）をフーリエ級数展開し、その各周波数成分に対して振幅を１／ｆｊ倍し、位相を−δｊだけずらした後、これらの和をとることにより、被測定物の表面プロフィールｍ（Ｘ）を求めることができる。このように、３点における測定値を用いて演算する方法を３点法という。
【００１５】
又、表面プロフィールを求める他の方法が特公平６−１５９７０号公報に開示されている。これは、被測定物表面に沿って等間隔で配置された複数個（ｎ個とする）の距離計を被測定物表面に沿って測定範囲の１／ｎの距離だけ移動させ、得られたｎ個の小区間におけるプロフィールを連結して、最終的に被測定物表面のプロフィールを求める方法である。この方法は、距離計の移動距離を短くすることができるため、測定時間の短縮を図ることができるという利点がある。
【００１６】
以下、図を用いて説明する。
【００１７】
図１４に示すように、短い間隔で配置された３個１組の（３点法）距離計１０Ａ、１０Ｂ、１０Ｃに加え、複数の距離計１０Ｄ、１０Ｅ、１０Ｆ、１０Ｇを距離計取付台１４に搭載し、被測定物表面１２ａまでの距離を測定する。このとき、５つの距離計１０Ｄ、１０Ｅ、１０Ｂ、１０Ｆ、１０Ｇは、被測定物１２の測定範囲Ｌに対し、Ｌ／５の間隔で等間隔に配置する。そして、３個１組の距離計１０Ａ、１０Ｂ、１０Ｃで３点法により求めた並進誤差とピッチング誤差を用いて他の４個の距離計１０Ｄ、１０Ｅ、１０Ｆ、１０Ｇの誤差を近似的に補正し、５個の距離計１０Ｄ、１０Ｅ、１０Ｂ、１０Ｆ、１０Ｇの誤差補正後のデータを連結することによって、最終的に表面プロフィールを求める。この方法では、距離計の移動量が測定範囲の１／５で済み、測定時間も約１／５に短縮することができる。
【００１８】
【発明が解決しようとする課題】
しかしながら、上記３点法には被測定物の表面プロフィールを多項式関数で表わした場合の２次成分（放物線形状）が正しく求まらないという問題がある。即ち、３点法では、表面プロフィールｍ（Ｘ）の２次成分が合成測定量Ｙ（Ｘ）では定数項に表われるが、一方で（６）式のように、３個の距離計１０Ａ、１０Ｂ、１０Ｃの先端部の図１３に示すような機械的不揃いΔｋによる影響項も上記合成測定量Ｙ（Ｘ）の定数項に表われる。Δｋを、例えば１０μｍオーダーの高精度で検出することは実質的に困難であり、又、一般にΔｋの値の方が表面プロフィールｍ（Ｘ）の２次成分項に比べて格段に大きい値となるため、表面プロフィールｍ（Ｘ）の２次成分を正しく求めることができない。
【００１９】
又、前記特公平６−１５９７０号公報に開示されている方法では、距離計の移動距離がＬ／５と短い分だけ、上記２次成分の誤差が全体の表面プロフィールに及ぼす影響が小さくなる。しかしながら、この方法では、以下に述べる問題がある。
【００２０】
図１４中の５個の距離計１０Ｄ、１０Ｅ、１０Ｂ、１０Ｆ、１０Ｇについての零点は一致していない場合が多く、その場合、図１５に実線で示すように、各距離計の測定データは隣り合う距離計の測定データと連続しない。そのため、図中に破線で示すように、例えば距離計１０Ｄの測定データの右端値に距離計１０Ｅの測定データの左端値が一致するように距離計１０Ｅの測定データをシフトさせ、距離計１０Ｂ、１０Ｆ、１０Ｇの測定データについても同様に、それぞれの左側の距離計データと連続するように順次シフトさせていく処理を行うことにより、全体のプロフィールを求めていた。しかし、例えば図１６に実線で示すように、距離計１０Ｅの測定データの左端に測定誤差があった場合、距離計１０Ｅの測定データをシフトさせる際に、誤差分だけ間違えた量をシフトさせてしまう。そのため、距離計１０Ｂ、１０Ｆ、１０Ｇの測定データのシフト量にも距離計１０Ｅの測定データの左端の誤差が反映され、測定位置Ｌ／５からＬまでの範囲では全体的に誤差が生じてしまう（図１６破線）という問題がある。
【００２１】
なお、上記３点法に限らず、一般に距離計を被測定物に沿って移動させながら測定した距離データから表面プロフィールを求める方法では、距離計の移動案内部の緩やかな変形（うねり）のため、あるいは被測定物表面プロフィールや周囲温度が時々刻々変化するような悪条件下での測定では、移動時間中における温度変化や被測定物表面プロフィール自体の変形のため、表面プロフィールの空間的低周波数成分（測定範囲全長にわたる緩やかなうねり形状）を精度良く測定することが困難であった。
【００２２】
本発明は、前記従来の問題に鑑みてさなれたものであり、正確な表面プロフィールを測定する技術を提供することを課題とする。
【００２３】
【課題を解決するための手段】
本発明は、被測定物に対し、該被測定物の表面測定方向に沿ってその両端を含む３ヶ所以上の位置に固定された３個以上の固定式変位検出器によって各固定式変位検出器から前記被測定物の表面までの距離を測定し、これらの測定値をもとに該被測定物の表面プロフィールの概形Ｐ１（Ｘ）を求めると共に、前記被測定物の表面測定方向に沿って移動する１個以上の移動式変位検出器によって、前記表面全体について該移動式変位検出器から該表面までの距離を測定し、この測定値から前記被測定物の表面プロフィールの候補Ｐ２（Ｘ）を求め、該表面プロフィールの候補Ｐ２（Ｘ）の空間的低周波数成分が前記表面プロフィールの概形Ｐ１（Ｘ）に一致するように表面プロフィールの候補Ｐ２（Ｘ）を補正することにより、前記被測定物の表面プロフィールを求めるようにして、前記課題を解決したものである。
【００２４】
本発明は又、被測定物に対し、該被測定物の表面測定方向に沿って、その両端を含む３ヶ所以上の位置に固定的に配置され、前記表面までの距離を測定する３個以上の固定式変位検出器と、前記被測定物の表面測定方向に沿って移動する変位検出器取付台に取り付けられ、前記表面までの距離を測定する１個以上の移動式変位検出器と、前記固定式変位検出器及び移動式変位検出器の測定値からそれぞれ表面プロフィールの概形Ｐ１（Ｘ）および表面プロフィールの候補Ｐ２（Ｘ）を求め、表面プロフィールの候補Ｐ２（Ｘ）の空間的低周波数成分が表面プロフィールの概形Ｐ１（Ｘ）に一致するように表面プロフィールの候補Ｐ２（Ｘ）を補正することにより表面プロフィールを算出する演算手段とを備えることにより、同様に前記課題を解決したものである。
【００２５】
本発明によれば、移動式変位検出器による測定値に加え、被測定物表面プロフィールの空間的低周波数成分を求めるため、３個以上の固定式変位検出器による測定値を用い、この固定式変位検出器による離散的な測定値を基準として、移動式変位検出器の測定値を補正するようにしたため、正確な表面プロフィールの測定が可能となった。
【００２６】
又、前記固定式変位検出器をほぼ等間隔で３個以上配置し、前記変位検出器取付台上に３個の移動式変位検出器を短い間隔でほぼ等間隔に取り付けた場合には、前記３個の移動式変位検出器に例えば３点法等を適用して求めた表面プロフィールを、前記固定式変位検出器による離散的な測定値を基準として補正するようにして、正確な表面プロフィールを測定することができる。
【００２７】
又、前記固定式変位検出器を被測定物の測定範囲の両端及び中央に各１個ずつ配置し、前記変位検出器取付台上両端に、それぞれ３個１組の移動式変位検出器を、各組の中央の変位検出器同士の間隔が被測定物の測定範囲の１／２となるように取り付けた場合には、前記移動式変位検出器の移動距離を短くして正確に表面プロフィールを測定することができる。
【００２８】
【発明の実施の形態】
以下、図面を参照して本発明の実施の形態を詳細に説明する。
【００２９】
図１は、本発明の第１実施形態に係る表面プロフィール測定装置の概略構成図である。図１に示すように、被測定物２２の表面２２ａに沿って距離計架台２６を設置し、この距離計架台２６上の、被測定物表面２２ａの両端部、中央部及びそれらの中間に対応する位置に５個の固定式距離計（固定式変位検出器）２０Ｄ、２０Ｅ、２０Ｆ、２０Ｇ、２０Ｈを設置する。このとき、測定範囲をＬとするとき、各固定式距離計の配置間隔は全て等間隔でＬ／４とする。又、この距離計架台２６上に、移動式距離計取付台２４を搭載し、これに３個の移動式距離計（移動式変位検出器）２０Ａ、２０Ｂ、２０Ｃを短い間隔、例えばＬ／１００で等間隔に設置する。この移動式距離計取付台２４は、距離計移動手段２８により被測定物表面２２ａに沿って距離０から距離Ｌまで移動可能となっている。上記５個の固定式距離計２０Ｄ、２０Ｅ、２０Ｆ、２０Ｇ、２０Ｈ及び３個の移動式距離計２０Ａ、２０Ｂ、２０Ｃの測定値は、図示しない演算手段に伝送され、演算手段ではこれらの値から表面プロフィールを算出する。
【００３０】
なお、距離計の種類としては接触式の距離計あるいはレーザ、渦電流、超音波等を利用した非接触式の距離計でもよく、被測定物２２及び測定環境に応じて適当なものを用いることができる。又、固定式距離計の個数は５個に限定されるものではなく、被測定物表面プロフィールの特性及び移動式距離計の個数等によって３個以上の適当な数に選定することができる。又、移動式距離計の個数や配置間隔も被測定物表面の全面を測定できる限りにおいては、適当に選択することができる。
【００３１】
以下、図２〜図８に基づいて第１実施形態による表面プロフィール測定方法を説明する。以下では、被測定物表面２２ａに沿う座標をｘ（測定範囲０≦ｘ≦Ｌ）、表面プロフィールを表わす座標をｙとし、測定物表面２２ａに沿う各位置における表面プロフィールを２次元座標（ｘ，ｙ）で表わす。
【００３２】
予め移動式距離計取付台２４を、例えば図１の左端（ｘ＝０）に移動しておき、距離計移動手段２８により、これを図１の右方向に距離Ｌまで移動させながら、移動式距離計２０Ａ、２０Ｂ、２０Ｃ及び固定式距離計２０Ｄ、２０Ｅ、２０Ｆ、２０Ｇ、２０Ｈで被測定物表面２２ａまでの距離を測定する。
【００３３】
図２に示すように、５個の固定式距離計２０Ｄ、２０Ｅ、２０Ｆ、２０Ｇ、２０Ｈの測定値ｙ１、ｙ２、ｙ３、ｙ４、ｙ５が得られたとする。これより、図３に示すように、両端部を基準（０）とした表面プロフィールの骨子となる５個の離散点Ｑ１（０，０）、Ｑ２（Ｌ／４，ｑ２）、Ｑ３（Ｌ／２，ｑ３）、Ｑ４（３Ｌ／４，ｑ４）、Ｑ５（Ｌ，０）を算出する。ここで、ｑ２、ｑ３、ｑ４は次の（１０）、（１１）、（１２）式から算出される。
【００３４】
ｑ２＝ｙ２−（ｙ１×３＋ｙ５）／４ …（１０）
ｑ３＝ｙ３−（ｙ１＋ｙ５）／２ …（１１）
ｑ４＝ｙ４−（ｙ１＋ｙ５×３）／４ …（１２）
【００３５】
そして、５点Ｑ１、Ｑ２、Ｑ３、Ｑ４、Ｑ５を通る図４に示すような２次曲線Ｐ１（ｘ）を最小自乗法で求める。
【００３６】
一方、移動式距離計２０Ａ、２０Ｂ、２０Ｃに３点法を適用して並進誤差及びピッチング誤差を除去し、図５に示すような表面プロフィールＰ２（ｘ）（０≦ｘ≦Ｌ）を求める。前に述べたように、この表面プロフィールＰ２（ｘ）は実際の表面プロフィールの２次成分形状を正しく表わしていない。そこで、表面プロフィールＰ２（ｘ）から２次関数成分を除去したＰ２′（ｘ）を算出する。
【００３７】
即ち、まずＰ２（ｘ）の図６に示すような２次成分Ｐ^＊ ２（ｘ）を最小自乗法で求める。これは、表面プロフィールＰ２（ｘ）に２次関数を最小自乗フィッティングしたものをＰ^＊ ２（ｘ）とすればよい。
【００３８】
次に、図７に示すように、Ｐ２′（ｘ）＝Ｐ２（ｘ）−Ｐ^＊ ２（ｘ）としてＰ２（ｘ）から２次関数成分を除去したＰ２′（ｘ）を算出する。次に、両端の点Ｐ２′（０）、Ｐ２′（Ｌ）が０になるようにＰ２′（ｘ）のレベリングを行う。
【００３９】
求める表面プロフィールｍ（ｘ）は、ｍ（ｘ）＝Ｐ２′（ｘ）＋Ｐ１（ｘ）として求められる。こうして求められた表面プロフィールｍ（ｘ）を図８に示す。
【００４０】
なお、上の例では移動式距離計の空間的低周波数成分を２次関数と見做してデータ処理する方法を示したが、２次関数でなく、例えば４次関数であっても良いし、又測定範囲を１周期とする三角関数（例えばｃｏｓ ）等であっても良く、本発明の主旨と相違しなければ差支えない。又、本実施形態ではＰ２（ｘ）を求めるのに３点法を用いたが、並進誤差及びピッチング誤差を除去する方法であれば３点法に限定されるものではない。又、並進誤差及びピッチング誤差が無視できるような場合には、移動式距離計の数は３個ではなく例えば１個であっても差支えない。
【００４１】
次に本発明の第２実施形態について説明する。
【００４２】
図９は、本発明の第２実施形態に係る表面プロフィール測定装置の概略構成図である。
【００４３】
図９に示すように、第２実施形態では測定範囲をＬとするとき、距離計架台３６上に等間隔でＬ／２で３個の固定式距離計３０Ｄ、３０Ｅ、３０Ｆを配置し、６個の移動式距離計３０Ａ、３０Ｂ、３０Ｃと３１Ａ、３１Ｂ、３１Ｃを３個ずつ２組に分けて、これら２組の距離計を間隔Ｌ／２で移動式距離計取付台３４上に設置している。移動式距離計取付台３４は、距離計移動手段３８により距離Ｌ／２だけ被測定物表面３２ａに沿って移動可能である。
【００４４】
本実施形態では、固定式距離計３０Ｄ、３０Ｅ、３０Ｆにより表面プロフィールの骨子となる３個の離散点Ｑ１、（０、０）、Ｑ２（Ｌ／２、ｙ２−（ｙ１＋ｙ３）／２）、Ｑ３（Ｌ、０）を求めると共に（ｙ１、ｙ２、ｙ３はそれぞれ固定式距離計３０Ｄ、３０Ｅ、３０Ｆの測定値である）、３個の距離計３０Ａ、３０Ｂ、３０Ｃの測定値に３点法等を適用して区間０≦ｘ≦Ｌ／２における表面プロフィールＰ２１（ｘ）を求め、３つの距離計３１Ａ、３１Ｂ、３１Ｃの測定値に３点法等を適用して区間Ｌ／２≦ｘ≦Ｌにおける表面プロフィールＰ２２（ｘ）をそれぞれ求める。
【００４５】
その後、Ｐ２１（０）がＱ１に、Ｐ２１（Ｌ／２）がＱ２に一致するようにＰ２１（ｘ）を平行移動あるいは回転移動し、又Ｐ２２（Ｌ／２）がＱ２に、Ｐ２２（Ｌ）がＱ３に一致するようにＰ２２（ｘ）を平行移動あるいは回転移動し、これらを単純に繋ぎ合わせれば各距離計の零点（オフセット量）の相違が解消された正確な表面プロフィールを得ることができる。
【００４６】
このような手順で固定式距離計によって測定された離散点を基準として、移動式距離計のデータを連結することにより、各距離計の両端部のデータの誤差に拘らず、被測定物全長に亘る表面プロフィールが正確に求められる。
【００４７】
なお、距離計移動手段による移動速度が一定と見做せない場合は、移動式距離計で測定した各々のデータが被測定物表面のどの位置で測定したものかがわかるように移動距離を検出し、それを距離計測定データと対応付ける手段を設ければ良い。
【００４８】
又、距離計架台が測定中に熱変形をする等の理由により剛体と見做せない場合には、ワイヤやレーザ光線等を基準として測定架台自体の変形量を別途検出し、架台の変形量を補正して表面プロフィールを算出するようにすれば良い。
【００４９】
【実施例】
以下、本発明の更に具体的な実施例を示す。
【００５０】
本実施例では、装置構成として図１に示したものを用いる。被測定物２２としては、長さ２０５０ｍｍ（Ｌ＝２０５０ｍｍ）の鉄鋼の圧延工程に用いる圧延ロールであり、固定式距離計及び移動式距離計としては、いずれも水柱式超音波距離計を、又距離計移動手段としては油圧シリンダを用いた。又、３個の移動式距離計の測定値から並進誤差及びピッチング誤差を除去するために３点法を用いた。
【００５１】
本実施例による測定結果を図１０に示す。図１０において、本実施例による測定結果は太線Ａで表わされており、又真の表面プロフィール（接触式距離計及びキャリパーで測定したもの）を細線Ｂで示す。又、従来法（固定式距離計を使わない方法）による測定結果を破線Ｃで示す。図１０が示すように従来法では検出不可能であった圧延ロールの中央部の膨み（ロールクラウン）は本実施例による装置及び方法によって精度良く測定できることがわかる。
【００５２】
【発明の効果】
以上説明したとおり本発明によれば、従来の移動式距離計による測定値に加え、被測定物表面プロフィールの空間的低周波数成分を求めるため、３個以上の固定式距離計による測定値を用い、この固定式距離計による離散的な測定値を基準として移動式距離計の測定値を補正するようにしたため、従来法では測定誤差の大きかった空間的低周波数成分を含め、正確な表面プロフィールを測定することが可能となった。
【図面の簡単な説明】
【図１】本発明の第１実施形態に係る表面プロフィールの測定装置の概略構成図
【図２】第１実施形態の固定式距離計の測定値を示すグラフ
【図３】同じく固定式距離計の測定値から得られた離散点を示すグラフ
【図４】図３の離散点を２次曲線で近似した線図
【図５】第１実施形態の移動式距離計の測定値を示す線図
【図６】図５に示す測定値から求めた２次成分を示す線図
【図７】図５の測定値から２次関数成分を除去した表面プロフィールを示す線図
【図８】第１実施形態によって求められた表面プロフィールを示す線図
【図９】本発明の第２実施形態に係る表面プロフィール測定装置の概略構成図
【図１０】本発明の１実施形態による測定結果を示す線図
【図１１】従来の表面プロフィール測定装置を示す概略構成図
【図１２】表面プロフィール測定における測定誤差を示す模式図
【図１３】従来の表面プロフィール測定装置による３点法の測定原理を示す模式図
【図１４】従来の別の表面プロフィール測定方法の測定装置を示す模式図
【図１５】従来の別の表面プロフィール測定方法における表面プロフィール測定データを示すグラフ
【図１６】従来の別の表面プロフィール測定方法における表面プロフィール測定データを示すグラフ
【符号の説明】
２０Ａ、２０Ｂ、２０Ｃ、２０Ｄ、２０Ｅ、２０Ｆ、２０Ｇ、２０Ｈ…距離計（変位検出器）
２２…被測定物
２２ａ…被測定物表面
２４…移動式距離計取付台
２６…距離計架台
２８…距離計移動手段[0001]
TECHNICAL FIELD OF THE INVENTION
The present invention relates to a technique for measuring the surface profile or straightness of an object to be measured, and particularly to a technique for measuring the surface profile of a long object under an environment having many disturbance factors such as vibration and temperature change, such as a roll of metal. The present invention relates to a method and an apparatus for measuring a surface profile, which are suitable for measuring with accuracy.
[0002]
[Prior art]
Conventionally, as a technique for measuring a surface profile of an object to be measured, as shown in FIG. 11, a distance meter in which one or a plurality of distance meters (displacement detectors) 10 are arranged substantially parallel to an object to be measured 12. It is installed on the side of the mounting base 14 facing the object to be measured 12, and the distance meter mounting base 14 is moved relative to the object to be measured 12 along the surface to be measured 12 a until the surface of the object to be measured 12 a is moved. It is known that a distance is measured by each distance meter 10 and a surface profile of the surface 12a of the object to be measured is obtained from these measured values.
[0003]
At this time, as shown in FIG. 12, the translation error Ez caused by the distance meter mounting base 14 approaching or moving away from the device under test 12 during movement, and the inclination of the distance meter mounting base 14 with respect to the moving direction during movement are reduced. The pitching error Ep caused by the change significantly reduces the accuracy of the profile measurement. Therefore, it is important to remove the translation error Ez and the pitching error Ep generated during the movement of the rangefinder mount 14 by any method in order to improve the measurement accuracy of the profile.
[0004]
As a method of removing these errors, for example, the literature "Paper Collection of Academic Lectures, Spring Meeting of the Japan Society of Precision Engineering, 1987", page 167, and the "three-point method" described in JP-A-64-61605, etc. well known. Hereinafter, the three-point method will be described.
[0005]
FIG. 13 is a schematic diagram showing the measurement principle of the three-point method. In the three-point method, three distance meters 10A, 10B, and 10C are installed on the distance meter mount 14 at intervals La and Lb, respectively. The distance meter mount 14 is moved along the surface 12a of the object to be measured, and the distance to the surface 12a of the object to be measured is measured. At this time, the moving direction of the distance meter mounting base 14 is set as the X axis, and the measured values yA (X), yB (X), yC of the respective distance meters 10A, 10B, 10C at the position of the moving distance X from the measurement start position. (X) is obtained. The rotation center of the pitching movement during the movement of the distance meter mount 14 is set at the position of the distance meter 10B, the surface profile shape of the surface 12a to be measured is m (X), and the translation error at the position of the movement distance X is Ez ( X), and the pitching error at the position of the movement distance X is Ep (X). Further, the mechanical displacement amounts of the detection units of the respective distance meters 10A, 10B, and 10C are assumed to be kA, kB, and kC, respectively. At this time, the following equations (1) to (3) hold between these measured values and the above-mentioned error and the like.
[0006]

[0007]
Here, assuming that a = −Lb / (La + Lb), b = −La / (La + Lb) and Δk = kB + a · kA + b · kC, a is multiplied by the equation (1), b is multiplied by the equation (3), and (1) , (2), and (3) are added to eliminate the translation error Ez (X) and the pitching error Ep (X), thereby obtaining a combined measured quantity Y (X) as shown in the following equation (4). Can be
[0008]

[0009]
Also, suppose that the length of the object to be measured 12 is L, and the surface profile shape m (X) is represented by the sum of Fourier series as shown in the following equation (5).
[0010]
(Equation 1)

[0011]
When the equation (5) is substituted into the equation (4) and arranged, the following equations (6) to (9) are obtained.
[0012]
(Equation 2)

[0013]

[0014]
Since fj and δj in the equations (7) and (8) are constants not depending on the surface profile m (X) of the measured object, the data sequence Y (X) obtained from the measured values is subjected to Fourier series expansion, and each frequency component thereof is obtained. After multiplying the amplitude by 1 / fj and shifting the phase by −δj, the surface profile m (X) of the measured object can be obtained by taking the sum of them. Such a method of calculating using the measured values at three points is called a three-point method.
[0015]
Another method for obtaining a surface profile is disclosed in Japanese Patent Publication No. 6-15970. This was obtained by moving a plurality (n) of distance meters arranged at equal intervals along the surface of the object to be measured by a distance of 1 / n of the measurement range along the surface of the object to be measured. This is a method of connecting profiles in n small sections to finally obtain a profile of the surface of the measured object. This method has an advantage that the measurement time can be shortened because the moving distance of the range finder can be shortened.
[0016]
This will be described below with reference to the drawings.
[0017]
As shown in FIG. 14, in addition to a set of three (three-point method) distance meters 10A, 10B, and 10C arranged at short intervals, a plurality of distance meters 10D, 10E, 10F, and 10G are attached to a distance meter mounting base 14. And measures the distance to the surface 12a of the object to be measured. At this time, the five rangefinders 10D, 10E, 10B, 10F, and 10G are arranged at equal intervals of L / 5 with respect to the measurement range L of the DUT 12. Then, the errors of the other four distance meters 10D, 10E, 10F, and 10G are approximately corrected using the translation error and the pitching error obtained by the three-point method with one set of three distance meters 10A, 10B, and 10C. Then, the surface profiles are finally determined by connecting the error-corrected data of the five rangefinders 10D, 10E, 10B, 10F, and 10G. In this method, the moving distance of the rangefinder is only 1/5 of the measuring range, and the measuring time can be reduced to about 1/5.
[0018]
[Problems to be solved by the invention]
However, the three-point method has a problem in that the quadratic component (parabolic shape) when the surface profile of the measured object is represented by a polynomial function cannot be determined correctly. That is, in the three-point method, the secondary component of the surface profile m (X) appears as a constant term in the combined measured amount Y (X), but on the other hand, as shown in equation (6), the three rangefinders 10A, Influence terms due to mechanical irregularities Δk at the tips of 10B and 10C as shown in FIG. 13 also appear in the constant term of the combined measured amount Y (X). It is substantially difficult to detect Δk with high accuracy, for example, on the order of 10 μm, and in general, the value of Δk is much larger than the second-order component term of the surface profile m (X). Therefore, the secondary component of the surface profile m (X) cannot be correctly obtained.
[0019]
Further, in the method disclosed in Japanese Patent Publication No. 6-15970, the influence of the error of the secondary component on the entire surface profile is reduced as the moving distance of the range finder is as short as L / 5. However, this method has the following problems.
[0020]
In many cases, the zeros of the five distance meters 10D, 10E, 10B, 10F, and 10G in FIG. 14 do not match, and in this case, as shown by the solid line in FIG. It is not continuous with the measurement data of the distance meter that fits. Therefore, as shown by a broken line in the figure, for example, the measurement data of the distance meter 10E is shifted so that the left end value of the measurement data of the distance meter 10E matches the right end value of the measurement data of the distance meter 10D, and the distance meter 10B, Similarly, with respect to the measurement data of 10F and 10G, similarly, the entire profile is obtained by performing a process of sequentially shifting the data so as to be continuous with the respective rangefinder data on the left side. However, for example, as shown by the solid line in FIG. 16, when there is a measurement error at the left end of the measurement data of the distance meter 10E, when shifting the measurement data of the distance meter 10E, the wrong amount is shifted by the error. I will. For this reason, the error at the left end of the measurement data of the distance meter 10E is also reflected in the shift amount of the measurement data of the distance meters 10B, 10F, and 10G, and an error occurs entirely in the range from the measurement position L / 5 to L. (Broken line in FIG. 16).
[0021]
In addition to the three-point method described above, in general, a method of obtaining a surface profile from distance data measured while moving a distance meter along an object to be measured is due to gradual deformation (undulation) of a movement guide portion of the distance meter. In the measurement under adverse conditions where the surface profile of the DUT and the ambient temperature change every moment, the spatial low frequency of the surface profile may be reduced due to temperature changes during the movement time and deformation of the DUT surface profile itself. It was difficult to accurately measure the component (a gently undulating shape over the entire measurement range).
[0022]
The present invention has been made in view of the above-described conventional problems, and has as its object to provide a technique for measuring an accurate surface profile.
[0023]
[Means for Solving the Problems]
The present invention provides each fixed displacement detector with three or more fixed displacement detectors fixed to three or more positions including both ends of the measured object along the surface measurement direction of the measured object. Is measured from the distance to the surface of the object to be measured, and based on these measured values, the approximate shape P1 (X) of the surface profile of the object to be measured is determined, and along the surface measurement direction of the object to be measured. The distance from the movable displacement detector to the surface over the entire surface is measured by one or more movable displacement detectors that move along the surface, and a candidate P2 (X ) And correcting the surface profile candidate P2 (X) such that the spatial low-frequency component of the surface profile candidate P2 (X) matches the general shape P1 (X) of the surface profile. Of the measured object So as to obtain the surface profile is obtained by solving the above problems.
[0024]
The present invention also provides three or more measurement objects, which are fixedly arranged at three or more positions including both ends thereof along the surface measurement direction of the measurement object and measure the distance to the surface. A fixed displacement detector, and one or more movable displacement detectors attached to a displacement detector mount that moves along the surface measurement direction of the object to be measured and measures a distance to the surface ; The surface profile outline P1 (X) and the surface profile candidate P2 (X) are obtained from the measured values of the fixed displacement detector and the mobile displacement detector, respectively, and the spatial low frequency of the surface profile candidate P2 (X) is obtained. by component and a calculating means for calculating the surface profile by correcting a candidate P2 (X) of the surface profile to match the approximate shape P1 (X) of the surface profile, the problems in the same manner Is that persists.
[0025]
According to the present invention, in order to determine the spatial low-frequency component of the surface profile of an object to be measured, in addition to the measurement value obtained by the mobile displacement detector, the measurement value obtained by using three or more fixed displacement detectors is used. Since the measured values of the mobile displacement detector are corrected based on the discrete measured values of the displacement detector, accurate measurement of the surface profile is possible.
[0026]
Further, when three or more fixed displacement detectors are disposed at substantially equal intervals, and three movable displacement detectors are mounted on the displacement detector mounting base at short intervals at substantially equal intervals, An accurate surface profile is obtained by correcting a surface profile obtained by applying, for example, a three-point method to three mobile displacement detectors based on discrete measurement values obtained by the fixed displacement detector. Can be measured.
[0027]
Further, one fixed displacement detector is disposed at each of both ends and the center of the measurement range of the object to be measured, and a set of three movable displacement detectors is provided at both ends on the displacement detector mounting table, respectively. When the distance between the displacement detectors at the center of each set is set to be １ ／ of the measurement range of the object to be measured, the moving distance of the movable displacement detector is shortened to accurately adjust the surface profile. Can be measured.
[0028]
BEST MODE FOR CARRYING OUT THE INVENTION
Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings.
[0029]
FIG. 1 is a schematic configuration diagram of a surface profile measuring device according to a first embodiment of the present invention. As shown in FIG. 1, a distance measuring stand 26 is installed along the surface 22a of the measured object 22, and the distance measuring stand 26 corresponds to both ends, the center, and the middle of the measured object surface 22a. 5 fixed distance meters (fixed displacement detectors) 20D, 20E, 20F, 20G, and 20H are installed at the positions where they are to be performed. At this time, when the measurement range is L, the arrangement intervals of the fixed rangefinders are all equal to L / 4. A movable distance meter mounting base 24 is mounted on the distance meter base 26, and three movable distance meters (movable displacement detectors) 20A, 20B, and 20C are mounted on this mount at short intervals, for example, L / 100. At equal intervals. The movable rangefinder mount 24 can be moved from the distance 0 to the distance L along the surface 22a of the measured object by the rangefinder moving means 28. The measured values of the five fixed rangefinders 20D, 20E, 20F, 20G, and 20H and the three mobile rangefinders 20A, 20B, and 20C are transmitted to calculation means (not shown). Calculate the surface profile.
[0030]
The type of the distance meter may be a contact type distance meter or a non-contact type distance meter using laser, eddy current, ultrasonic wave, or the like, and an appropriate one may be used according to the measured object 22 and the measurement environment. Can be. The number of fixed rangefinders is not limited to five, but may be selected to be three or more depending on the characteristics of the surface profile of the object to be measured and the number of mobile rangefinders. Further, the number and the arrangement interval of the movable distance meters can be appropriately selected as long as the entire surface of the object to be measured can be measured.
[0031]
Hereinafter, a method of measuring a surface profile according to the first embodiment will be described with reference to FIGS. Hereinafter, the coordinates along the workpiece surface 22a are x (measurement range 0 ≦ x ≦ L), the coordinates representing the surface profile are y, and the surface profile at each position along the workpiece surface 22a is two-dimensional coordinates (x, y).
[0032]
The movable distance meter mounting base 24 has been previously moved to, for example, the left end (x = 0) in FIG. 1, and the movable distance meter mounting means 24 is moved rightward in FIG. The distance to the measured object surface 22a is measured by the distance meters 20A, 20B, 20C and the fixed distance meters 20D, 20E, 20F, 20G, 20H.
[0033]
As shown in FIG. 2, it is assumed that measured values y1, y2, y3, y4, and y5 of five fixed rangefinders 20D, 20E, 20F, 20G, and 20H are obtained. From this, as shown in FIG. 3, the five discrete points Q1 (0, 0), Q2 (L / 4, q2), and Q3 (L / 2, q3), Q4 (3L / 4, q4), and Q5 (L, 0) are calculated. Here, q2, q3, and q4 are calculated from the following equations (10), (11), and (12).
[0034]
q2 = y2- (y1 × 3 + y5) / 4 (10)
q3 = y3- (y1 + y5) / 2 (11)
q4 = y4- (y1 + y5 × 3) / 4 (12)
[0035]
Then, a quadratic curve P1 (x) passing through the five points Q1, Q2, Q3, Q4, and Q5 as shown in FIG. 4 is obtained by the least square method.
[0036]
On the other hand, the translational error and the pitching error are removed by applying the three-point method to the movable distance meters 20A, 20B, and 20C, and the surface profile P2 (x) (0 ≦ x ≦ L) as shown in FIG. 5 is obtained. As mentioned earlier, this surface profile P2 (x) does not correctly represent the quadratic component shape of the actual surface profile. Therefore, P2 '(x) is calculated by removing the quadratic function component from the surface profile P2 (x).
[0037]
That is, first, a secondary component P ^* 2 (x) of P2 (x) as shown in FIG. 6 is obtained by the least square method. This can be achieved by making a quadratic function least square fitting the surface profile P2 (x) be P ^* 2 (x).
[0038]
Next, as shown in FIG. 7, as P2 '(x) = P2 (x) -P ^* 2 (x), P2' (x) obtained by removing the quadratic function component from P2 (x) is calculated. Next, leveling of P2 '(x) is performed so that the points P2' (0) and P2 '(L) at both ends become 0.
[0039]
The required surface profile m (x) is obtained as m (x) = P2 '(x) + P1 (x). FIG. 8 shows the surface profile m (x) thus obtained.
[0040]
In the above example, a method of performing data processing by regarding the spatial low-frequency component of the mobile distance meter as a quadratic function has been described, but may be a quadratic function instead of a quadratic function. Alternatively, a trigonometric function (for example, cos) having a measurement range of one cycle may be used. In the present embodiment, the three-point method is used to obtain P2 (x). However, the method is not limited to the three-point method as long as the method eliminates the translation error and the pitching error. If the translation error and the pitching error are negligible, the number of mobile rangefinders may be one instead of three, for example.
[0041]
Next, a second embodiment of the present invention will be described.
[0042]
FIG. 9 is a schematic configuration diagram of a surface profile measuring device according to the second embodiment of the present invention.
[0043]
As shown in FIG. 9, when the measurement range is L in the second embodiment, three fixed distance meters 30D, 30E, and 30F are arranged at equal intervals on the distance meter stand 36 at L / 2, and 6 The mobile rangefinders 30A, 30B, 30C and 31A, 31B, 31C are divided into two sets of three each, and these two sets of rangefinders are installed on the mobile rangefinder mounting base 34 at an interval L / 2. ing. The movable distance meter mounting base 34 can be moved by the distance meter moving means 38 along the surface 32a of the object to be measured by a distance L / 2.
[0044]
In the present embodiment, three discrete points Q1, (0, 0), Q2 (L / 2, y2- (y1 + y3) / 2), Q3, which are the essence of the surface profile, by the fixed distance meters 30D, 30E, 30F. (L, 0) is obtained (y1, y2, and y3 are measured values of the fixed rangefinders 30D, 30E, and 30F, respectively), and the measured values of the three rangefinders 30A, 30B, and 30C are measured by a three-point method. Is applied to determine the surface profile P21 (x) in the section 0 ≦ x ≦ L / 2, and the section L / 2 ≦ x ≦ by applying the three-point method or the like to the measured values of the three distance meters 31A, 31B, 31C. The surface profile P22 (x) at L is obtained.
[0045]
Then, P21 (x) is translated or rotated so that P21 (0) matches Q1 and P21 (L / 2) matches Q2, and P22 (L / 2) changes to Q2 and P22 (L). If P22 (x) is translated or rotated so as to coincide with Q3 and these are simply connected, an accurate surface profile in which the difference in the zero point (offset amount) of each distance meter has been eliminated can be obtained. .
[0046]
By linking the data of the mobile rangefinder to the discrete points measured by the fixed rangefinder in such a procedure, regardless of the error of the data at both ends of each rangefinder, An accurate surface profile is determined.
[0047]
If the moving speed by the range finder moving means cannot be considered to be constant, the moving distance is detected so that each data measured by the moving range finder can be determined at which position on the surface of the object to be measured. Then, means for associating the data with the distance measurement data may be provided.
[0048]
If the range finder stand cannot be regarded as a rigid body due to thermal deformation during measurement, etc., the deformation amount of the measurement stand itself is separately detected based on a wire, a laser beam, etc., and the deformation amount of the stand is measured. May be corrected to calculate the surface profile.
[0049]
【Example】
Hereinafter, more specific examples of the present invention will be described.
[0050]
In the present embodiment, the device configuration shown in FIG. 1 is used. The measurement object 22 is a rolling roll used in a rolling process of steel having a length of 2050 mm (L = 2050 mm). As the fixed distance meter and the movable distance meter, both are a water column type ultrasonic distance meter, and A hydraulic cylinder was used as the distance meter moving means. In addition, a three-point method was used to remove translation errors and pitching errors from the measured values of three mobile rangefinders.
[0051]
FIG. 10 shows the measurement results according to the present example. In FIG. 10, the measurement result according to the present embodiment is indicated by a thick line A, and the true surface profile (measured by a contact distance meter and a caliper) is indicated by a thin line B. A broken line C shows a measurement result by a conventional method (a method not using a fixed distance meter). As shown in FIG. 10, it can be seen that the swelling (roll crown) at the center of the rolling roll, which could not be detected by the conventional method, can be accurately measured by the apparatus and method according to the present embodiment.
[0052]
【The invention's effect】
As described above, according to the present invention, in addition to the values measured by the conventional mobile distance meter, the values measured by three or more fixed distance meters are used to determine the spatial low-frequency component of the surface profile of the measured object. Since the measurement value of the mobile distance meter is corrected based on the discrete measurement value of this fixed distance meter, the accurate surface profile including the spatial low-frequency component that had a large measurement error in the conventional method was obtained. It became possible to measure.
[Brief description of the drawings]
FIG. 1 is a schematic configuration diagram of an apparatus for measuring a surface profile according to a first embodiment of the present invention. FIG. 2 is a graph showing measured values of a fixed distance meter according to the first embodiment. FIG. 4 is a graph showing the discrete points obtained from the measured values of FIG. 4. FIG. 4 is a diagram in which the discrete points of FIG. 3 are approximated by a quadratic curve. FIG. 5 is a diagram showing the measured values of the mobile distance meter of the first embodiment. 6 is a diagram showing a quadratic component obtained from the measurement values shown in FIG. 5; FIG. 7 is a diagram showing a surface profile obtained by removing a quadratic function component from the measurement values in FIG. 5; FIG. 9 is a schematic diagram showing a surface profile measurement device according to a second embodiment of the present invention. FIG. 10 is a schematic diagram showing a measurement result according to an embodiment of the present invention. FIG. 11 is a schematic configuration diagram showing a conventional surface profile measuring apparatus. FIG. 13 is a schematic diagram showing a measurement error in lofil measurement. FIG. 13 is a schematic diagram showing a measurement principle of a three-point method using a conventional surface profile measuring device. FIG. 14 is a schematic diagram showing a measuring device of another conventional surface profile measuring method. FIG. 15 is a graph showing surface profile measurement data in another conventional surface profile measurement method. FIG. 16 is a graph showing surface profile measurement data in another conventional surface profile measurement method.
20A, 20B, 20C, 20D, 20E, 20F, 20G, 20H ... distance meter (displacement detector)
Reference numeral 22: DUT 22a: Surface of the DUT 24: Movable rangefinder mount 26: Rangefinder stand 28: Rangefinder moving means

Claims (4)

The object to be measured is measured from each of the fixed displacement detectors by three or more fixed displacement detectors fixed at three or more positions including both ends thereof along the surface measurement direction of the object to be measured. The distance to the surface of the object is measured, and based on these measured values, the approximate shape P1 (X) of the surface profile of the object is determined.
The distance from the mobile displacement detector to the surface is measured for the entire surface by one or more mobile displacement detectors moving along the surface measurement direction of the object, and the measured A candidate P2 (X) of the surface profile of the measurement object is determined, and the candidate P2 of the surface profile is set such that the spatial low-frequency component of the candidate P2 (X) of the surface profile matches the general shape P1 (X) of the surface profile. A method of measuring a surface profile, wherein a surface profile of the object is obtained by correcting (X). Three or more fixed displacement detectors which are fixedly arranged at three or more positions including both ends of the object to be measured along the surface measurement direction of the object to measure the distance to the surface. Vessels,
One or more movable displacement detectors attached to a displacement detector mount that moves along the surface measurement direction of the object to be measured and measures a distance to the surface ;
From the measured values of the fixed displacement detector and the mobile displacement detector, the approximate shape P1 (X) of the surface profile and the candidate P2 (X) of the surface profile are obtained, and the spatial profile of the candidate P2 (X) of the surface profile is calculated. Calculating means for calculating the surface profile by correcting the surface profile candidate P2 (X) such that the frequency component matches the outline P1 (X) of the surface profile;
Surface profile measuring apparatus characterized by comprising a. 3. The method according to claim 2, wherein three or more fixed displacement detectors are arranged at substantially equal intervals, and three movable displacement detectors are mounted on the displacement detector mounting base at substantially equal intervals at short intervals. Characterized surface profile measurement device. 3. The displacement detector according to claim 2, wherein one fixed displacement detector is disposed at each of both ends and a center of the measurement range of the object to be measured, and a set of three movable displacement detectors is provided at both ends on the displacement detector mounting base. A surface profile measuring device, wherein instruments are mounted such that a distance between central displacement detectors of each set is １ ／ of a measuring range of an object to be measured.

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